According to the Current Results website, the state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 54 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. Use z-table. a. Show the probability distribution of the sample mean annual rainfall for California. This is a normal probability distribution with E(7) 22 and oz = 4 (to 4 decimals). b. What is the probability that the sample mean is within 1 inch of the population mean for California? (to 4 decimals) c. What is the probability that the sample mean is within 1 inch of the population mean for New York? (to 4 decimals) d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why? The probability of being within 1 inch is greater for New York in part (c) v because the sample size is larger

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According to the Current Results website, the state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual
rainfall of 54 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of
rainfall for New York has been taken. Use z-table.
a. Show the probability distribution of the sample mean annual rainfall for California.
This is a normal probability distribution with E() =
22 and oz =
4 (to 4 decimals).
b. What is the probability that the sample mean is within 1 inch of the population mean for California?
(to 4 decimals)
c. What is the probability that the sample mean is within 1 inch of the population mean for New York?
(to 4 decimals)
d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?
The probability of being within 1 inch is greater for New York in part (c) ♥ because the sample size is larger
Transcribed Image Text:According to the Current Results website, the state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 54 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. Use z-table. a. Show the probability distribution of the sample mean annual rainfall for California. This is a normal probability distribution with E() = 22 and oz = 4 (to 4 decimals). b. What is the probability that the sample mean is within 1 inch of the population mean for California? (to 4 decimals) c. What is the probability that the sample mean is within 1 inch of the population mean for New York? (to 4 decimals) d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why? The probability of being within 1 inch is greater for New York in part (c) ♥ because the sample size is larger
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